The traveler's dilemma is a generalization of the prisoner's dilemma which shows clearly a paradox of game theory. In the traveler's dilemma, the strategy chosen by analysis and theory seems obviously wrong intuitively. Here we develop a measure of evolutionary stability and show that the evolutionarily stable equilibrium is in some sense not very stable. Understanding evolutionary stability on a continuum instead of as a yes-or-no definition helps to explain and partially resolve the paradox in the traveler's dilemma.